Bernoulli’s Equation is one of the most versatile equation ever.

This is an important principle involving the movement of a fluid through a pressure difference. Suppose a fluid is moving in a horizontal direction and encounters a pressure difference. This pressure difference will result in a net force, which by Newton’s 2nd law will cause an acceleration of the fluid. The fundamental relation,

in this situation can be written as-

which furthermore can be expressed as

In other words,

This principle is generally known as the **conservation of energy principle** and states that the **total energy** of an isolated system remains constant — it is said to be conserved over time. This is equivalent to the **First Law of Thermodynamics**, which is used to develop the general energy equation in thermodynamics. This principle can be used in the analysis of **flowing fluids **and this principle is expressed mathematically by the following equation:

where h is enthalpy, k is the thermal conductivity of the fluid, T is temperature, and Φ is the viscous dissipation function.

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